Loss of ergodicity in a quantum hopping model of a dense many body system with repulsive interactions

TL;DR

This paper investigates how a quantum hopping model, inspired by the Hubbard Hamiltonian, exhibits loss of ergodicity at high densities due to Pauli exclusion and Coulomb repulsion, affecting phase transitions and thermalization.

Contribution

It demonstrates the emergence of ergodicity loss in a quantum many-body system with strong interactions, linking Euclidean time behavior to real-time thermalization breakdown.

Findings

Ergodicity is lost at high densities in the model.

Quantum phase transitions depend on initial configurations.

Breakdown may relate to eigenstate thermalization hypothesis failure.

Abstract

In this work we report on a loss of ergodicity in a simple hopping model, motivated by the Hubbard Hamiltonian, of a many body quantum system at zero temperature, quantized in Euclidean time. We show that this quantum system may lose ergodicity at high densities on a large lattice, as a result of both Pauli exclusion and strong Coulomb repulsion. In particular we study particle hopping susceptibilities and the tendency towards particle localization. It is found that the appearance and existence of quantum phase transitions in this model, in the case of high density and strong Coulomb repulsion, depends on the starting configuration of particle trajectories in the numerical simulation. We argue that this breakdown may be the Euclidean time version of a breakdown of the eigenstate thermalization hypothesis in real time quantization.